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How Do You Find the Square Root of a Fraction?

What is the square root of 9/16?

Summary

  1. The definition of a square root starts out by defining 'a2=b'
  2. If 'a2=b', then the square root of 'b' equals 'a'!
  3. Since we are taking the square root of a fraction, break up the square root so you are taking the square root of the numerator and denominator separately
  4. 'The square root of 9' is '3', which means it's a perfect square
  5. 'The square root of 16' is '4', which means it is also a perfect square
  6. So 'the square root of 9/16' is '3/4'!

Notes

    1. 'a' and 'b' are variables here
    2. So if we know the value of 'a' or 'b', we can solve for the other variable!
    1. The definition of a square root says if 'a2=b', then the square root of 'b' equals 'a'
    2. In our given problem, '9/16' is equivalent to 'b' in our definition of a square root
    1. The definition of a square root says if 'a2=b', then the square root of 'b' equals 'a'
    2. In our given problem, '9/16' is equivalent to 'b' in our definition of a square root
    1. The definition of a square root says if 'a2=b', then the square root of 'b' equals 'a'
    2. In our given problem, '9/16' is equivalent to 'b' in our definition of a square root
    1. The definition of a square root says if 'a2=b', then the square root of 'b' equals 'a'
    2. In our given problem, '9/16' is equivalent to 'b' in our definition of a square root
    1. The definition of a square root says if 'a2=b', then the square root of 'b' equals 'a'
    2. In our given problem, '9/16' is equivalent to 'b' in our definition of a square root
    3. Since we're splitting up our square root into two, we will have two 'b' terms, '9' and '16'
    1. The definition of a square root says if 'a2=b', then the square root of 'b' equals 'a'
    2. In our given problem, '9/16' is equivalent to 'b' in our definition of a square root
    3. Since we're splitting up our square root into two, we will have two 'b' terms, '9' and '16'
    1. '9' and '16' are perfect squares
    1. '9' and '16' are perfect squares
    2. The 'square root of 9' is exactly '3'
    3. The 'square root of 16' is exactly '4'
    1. '9' and '16' are perfect squares
    2. The 'square root of 9' is exactly '3'
    3. The 'square root of 16' is exactly '4'
    4. We can rewrite 'the square root 9 over the square root of 16' as '3/4' , which is our answer
    1. We can rewrite 'the square root 9 over the square root of 16' as '3/4' , which is our answer
    1. We originally had 'the square root of 9/16'
    1. We originally had 'the square root of 9/16'
    1. We originally had 'the square root of 9/16', which we rewrote as 'the square root of 9 over the square root of 16'
    2. Since the 'b' terms '9' and '16' are perfect squares, we ended up with final answer of '3/4', where the 'a' terms are '3' and '4'